Field
This disclosure generally relates to designs, layouts, and architectures for quantum processors comprising qubits and techniques for operating the same.
Adiabatic Quantum Computation
Adiabatic quantum computation typically involves evolving a system from a known initial Hamiltonian (the Hamiltonian being an operator whose eigenvalues are the allowed energies of the system) to a final Hamiltonian by gradually changing the Hamiltonian. A simple example of an adiabatic evolution is a linear interpolation between initial Hamiltonian and final Hamiltonian. An example is given by:He=(1−s)Hi+sHf  (1)where Hi is the initial Hamiltonian, Hf is the final Hamiltonian, He is the evolution or instantaneous Hamiltonian, and s is an evolution coefficient which controls the rate of evolution. As the system evolves, the evolution coefficient s goes from 0 to 1 such that at the beginning (i.e., s=0) the evolution Hamiltonian He is equal to the initial Hamiltonian Hi and at the end (i.e., s=1) the evolution Hamiltonian He is equal to the final Hamiltonian Hf. Before the evolution begins, the system is typically initialized in a ground state of the initial Hamiltonian Hi and the goal is to evolve the system in such a way that the system ends up in a ground state of the final Hamiltonian Hf at the end of the evolution. If the evolution is too fast, then the system can transition to a higher energy state, such as the first excited state. In the present systems and devices, an “adiabatic” evolution is an evolution that satisfies the adiabatic condition:{dot over (s)}|1|dhe/ds|0|=δg2(s)  (2)where {dot over (s)} is the time derivative of s, g(s) is the difference in energy between the ground state and first excited state of the system (also referred to herein as the “gap size”) as a function of s, and δ is a coefficient much less than 1. Generally the initial Hamiltonian Hi and the final Hamiltonian Hf do not commute. That is, [Hi, Hf]≠0.
The process of changing the Hamiltonian in adiabatic quantum computing may be referred to as evolution. If the rate of change, for example, change of s, is slow enough that the system is always in the instantaneous ground state of the evolution Hamiltonian, then transitions at anti-crossings (i.e., when the gap size is smallest) are avoided. The example of a linear evolution schedule is given above. Other evolution schedules are possible including non-linear, parametric, and the like. Further details on adiabatic quantum computing systems, methods, and apparatus are described in, for example, U.S. Pat. Nos. 7,135,701; and 7,418,283.
Depending on the form of the final Hamiltonian and the way the final results are extracted, one can operate an adiabatic quantum computer in at least three different modes. First, the adiabatic quantum computer can be operated as an adiabatic quantum optimizer to find the ground states of a Hamiltonian. This is also called quantum annealing. Second, it can be operated as a quantum simulator. Third, it can be operated to achieve the results of a gate model quantum algorithm by mapping from the gate model algorithm to an algorithm in the adiabatic quantum computing model.
Quantum Annealing
Quantum annealing is a computation method that may be used to find a low-energy state, typically preferably the ground state, of a system. Similar in concept to classical annealing, the method relies on the underlying principle that natural systems tend towards lower energy states because lower energy states are more stable. However, while classical annealing uses classical thermal fluctuations to guide a system to a low-energy state and ideally its global energy minimum, quantum annealing may use quantum effects, such as quantum tunneling, to reach a global energy minimum more accurately and/or more quickly than classical annealing. In quantum annealing thermal effects and other noise may be present to aid the annealing. However, the final low-energy state may not be the global energy minimum. Adiabatic quantum computation, therefore, may be considered a special case of quantum annealing for which the system, ideally, begins and remains in its ground state throughout an adiabatic evolution. Thus, those of skill in the art will appreciate that quantum annealing systems and methods may generally be implemented on an adiabatic quantum computer. Throughout this specification and the appended claims, any reference to quantum annealing is intended to encompass adiabatic quantum computation unless the context requires otherwise.
Quantum annealing uses quantum mechanics as a source of disorder during the annealing process. The optimization problem is encoded in a Hamiltonian HP, and the algorithm introduces quantum effects by adding a disordering Hamiltonian HD that does not commute with HP. An example case is:HE∝A(t)HD+B(t)HP  (3)where A(t) and B(t) are time dependent envelope functions. For example, A(t) changes from a large value to substantially zero during the evolution and HE may be thought of as an evolution Hamiltonian similar to He described in the context of adiabatic quantum computation above. The disorder is slowly removed by removing HD (i.e., reducing A(t). Thus, quantum annealing is similar to adiabatic quantum computation in that the system starts with an initial Hamiltonian and evolves through an evolution Hamiltonian to a final “problem” Hamiltonian HP whose ground state encodes a solution to the problem. If the evolution is slow enough, the system may settle in the global minimum (i.e., the exact solution), or in a local minimum close in energy to the exact solution. The performance of the computation may be assessed via the residual energy (difference from exact solution using the objective function) versus evolution time. The computation time is the time required to generate a residual energy below some acceptable threshold value. In quantum annealing, HP may encode an optimization problem but the system does not necessarily stay in the ground state at all times. The energy landscape of Hp may be crafted so that its global minimum is the answer to the problem to be solved, and low-lying local minima are good approximations.Simulating Physics
Adiabatic quantum computation may also be used for quantum simulation. Quantum simulation was the original application of quantum computers, see for example, R. P. Feynman, 1982 “Simulating physics with computers” International journal of theoretical physics 21(6), 467. The Hamiltonian of a quantum system is mapped on the Hamiltonian of a multi-qubit system and defines the final or problem Hamiltonian. An initial or disordering Hamiltonian is present per adiabatic computing model. The ground state of the problem Hamilton is then reached via adiabatic evolution. Reading out the final state then provides information about the ground state of the simulated system. A ground-state energy is the lowest eigenvalue of a time-independent Schrödinger equation for the system. The Phase-Estimation Algorithm (PEA) provides the spectrum of the system being simulated via the application of various gates and measurements in accordance with the gate model of quantum computing. See D. S. Abrams and S. Lloyd, 1997 “Simulation of Many-Body Fermi Systems on a Universal Quantum Computer” Phys. Rev. Lett. 79, 2586; and D. S. Abrams and S. Lloyd, 1999 “Quantum Algorithm Providing Exponential Speed Increase for Finding Eigenvalues and Eigenvectors” Phys. Rev. Lett. 83, 5162.
Universal Quantum Computing
A quantum computational model is universal if it can solve a class of problems known as bounded-error quantum polynomial-time (BQP) problems in polynomial time. Such a universal computer is desirable. A quantum computer including qubits is known to be universal when it can perform single-qubit and non-local many-qubit operations. The operations should be unitary and the many qubit operations entangling. A universal quantum computer (UQC) may also be characterized as a quantum computer able to efficiently simulate any other quantum computer.
Superconducting Qubits
There are types of solid state qubits which are based on circuits of superconducting materials. There are two superconducting effects that underlie how superconducting qubits operate: magnetic flux quantization, and Josephson tunneling.
Flux is quantized via the Aharonov-Bohm effect where electrical charge carriers accrue a topological phase when traversing a conductive loop threaded by a magnetic flux. For superconducting loops, the charge carriers are pairs of electrons called Cooper pairs. For a loop of sufficiently thick superconducting material, quantum mechanics dictates that the Cooper pairs accrue a phase that is an integer multiple of 2π. This, then, constrains the allowed values of magnetic flux threading the loop.
Josephson tunneling is the process by which Cooper pairs cross an interruption, such as an insulating gap of a few nanometers, between two superconducting electrodes. The amount of current is sinusoidally dependent on the phase difference between the two populations of Cooper pairs in the electrodes. These superconducting effects are present in different configurations and give rise to different types of superconducting qubits including flux, phase, charge, and hybrid qubits. These different types of qubits depend on the topology of the loops, placement of the Josephson junctions, and the physical parameters of the parts of the circuit such as inductance, capacitance, and Josephson junction critical current.
Quantum Processor
A quantum processor may take the form of a superconducting quantum processor. A superconducting quantum processor may include a number of qubits and associated local bias devices, for instance two or more superconducting qubits. A superconducting quantum processor may also employ coupling devices (i.e., “couplers”) providing communicative coupling between qubits. A qubit and a coupler resemble each other but differ in physical parameters. One difference is the screening parameter, β. Consider an rf-SQUID, which includes a superconducting loop interrupted by Josephson junction. The screening parameter β is defined as the ratio of the geometrical inductance of the loop to the so called Josephson inductance of the junction.
The screening parameter β is defined as 2πLIC/Φ0. That is, β is proportional to the product of inductance and critical current. A design with lower values of β, below about 1, behaves more like an inductive loop whose magnetic susceptibility is altered by the presence of the Josephson junction. This is a monostable device. A design with higher values of β is more dominated by the Josephson junctions and produces a multistable behavior, such as bistable behavior. Flux qubits are typically designed to be bistable wherein there are degenerate ground state configurations for the superconducting current flowing around the loop. For SQUIDs with sufficiently low capacitance, quantum tunneling lifts the degeneracy of the ground state. Couplers are typically designed to be monostable, such that there is a single ground state configuration of the superconducting current flowing around the loop.
Both qubits and couplers can have more devices associated with them. Further details and embodiments of exemplary quantum processors that may be used in conjunction with the present systems and devices are described in, for example, U.S. Pat. Nos. 7,533,068; 8,008,942; 8,195,596; 8,190,548; and 8,421,053.
Most efforts in the field of quantum computing are devoted to the development of hardware that supports the universal quantum computing paradigm known as gate model quantum computation (GMQC). While GMQC has proved theoretically appealing, it has been difficult to realize in practice. An alternative quantum computing paradigm that has received appreciable experimental effort to date is adiabatic quantum computation (AQC).
Existing approaches to AQC include hardware that implements a particular AQC algorithm known as adiabatic quantum optimization (AQO). While AQO cannot provide the full functionality of what is deemed to be a universal quantum computer, it has nonetheless provided a valuable testing ground for the development of a quantum computing technology using currently available device fabrication techniques.
The quantum processor described herein takes what has been learned from building an AQO technology and applies that knowledge to the development of a universal quantum computer. The computational equivalence of AQC to GMQC has been shown in the art, and publications exist showing how to map exemplary algorithms from the gate model to the adiabatic quantum computing model.